115 research outputs found
Biaxial Nematic Order in Liver Tissue
Understanding how biological cells organize to form complex functional tissues is a question of key interest at the interface between biology and physics. The liver is a model system for a complex three-dimensional epithelial tissue, which performs many vital functions. Recent advances in imaging methods provide access to experimental data at the subcellular level. Structural details of individual cells in bulk tissues can be resolved, which prompts for new analysis methods. In this thesis, we use concepts from soft matter physics to elucidate and quantify structural properties of mouse liver tissue.
Epithelial cells are structurally anisotropic and possess a distinct apico-basal cell polarity that can be characterized, in most cases, by a vector. For the parenchymal cells of the liver (hepatocytes), however, this is not possible. We therefore develop a general method to characterize the distribution of membrane-bound proteins in cells using a multipole decomposition. We first verify that simple epithelial cells of the kidney are of vectorial cell polarity type and then show that hepatocytes are of second order (nematic) cell polarity type. We propose a method to quantify orientational order in curved geometries and reveal lobule-level patterns of aligned cell polarity axes in the liver. These lobule-level patterns follow, on average, streamlines defined by the locations of larger vessels running through the tissue. We show that this characterizes the liver as a nematic liquid crystal with biaxial order. We use the quantification of orientational order to investigate the effect of specific knock-down of the adhesion protein Integrin Ăź-1.
Building upon these observations, we study a model of nematic interactions. We find that interactions among neighboring cells alone cannot account for the observed ordering patterns. Instead, coupling to an external field yields cell polarity fields that closely resemble the experimental data. Furthermore, we analyze the structural properties of the two transport networks present in the liver (sinusoids and bile canaliculi) and identify a nematic alignment between the anisotropy of the sinusoid network and the nematic cell polarity of hepatocytes. We propose a minimal lattice-based model that captures essential characteristics of network organization in the liver by local rules. In conclusion, using data analysis and minimal theoretical models, we found that the liver constitutes an example of a living biaxial liquid crystal.:1. Introduction 1
1.1. From molecules to cells, tissues and organisms: multi-scale hierarchical organization in animals 1
1.2. The liver as a model system of complex three-dimensional tissue 2
1.3. Biology of tissues 5
1.4. Physics of tissues 9
1.4.1. Continuum descriptions 11
1.4.2. Discrete models 11
1.4.3. Two-dimensional case study: planar cell polarity in the fly wing 15
1.4.4. Challenges of three-dimensional models for liver tissue 16
1.5. Liquids, crystals and liquid crystals 16
1.5.1. The uniaxial nematic order parameter 19
1.5.2. The biaxial nematic ordering tensor 21
1.5.3. Continuum theory of nematic order 23
1.5.4. Smectic order 25
1.6. Three-dimensional imaging of liver tissue 26
1.7. Overview of the thesis 28
2. Characterizing cellular anisotropy 31
2.1. Classifying protein distributions on cell surfaces 31
2.1.1. Mode expansion to characterize distributions on the unit sphere 31
2.1.2. Vectorial and nematic classes of surface distributions 33
2.1.3. Cell polarity on non-spherical surfaces 34
2.2. Cell polarity in kidney and liver tissues 36
2.2.1. Kidney cells exhibit vectorial polarity 36
2.2.2. Hepatocytes exhibit nematic polarity 37
2.3. Local network anisotropy 40
2.4. Summary 41
3. Order parameters for tissue organization 43
3.1. Orientational order: quantifying biaxial phases 43
3.1.1. Biaxial nematic order parameters 45
3.1.2. Co-orientational order parameters 51
3.1.3. Invariants of moment tensors 52
3.1.4. Relation between these three schemes 53
3.1.5. Example: nematic coupling to an external field 55
3.2. A tissue-level reference field 59
3.3. Orientational order in inhomogeneous systems 62
3.4. Positional order: identifying signatures of smectic and columnar order 64
3.5. Summary 67
4. The liver lobule exhibits biaxial liquid-crystal order 69
4.1. Coarse-graining reveals nematic cell polarity patterns on the lobulelevel 69
4.2. Coarse-grained patterns match tissue-level reference field 73
4.3. Apical and basal nematic cell polarity are anti-correlated 74
4.4. Co-orientational order: nematic cell polarity is aligned with network anisotropy 76
4.5. RNAi knock-down perturbs orientational order in liver tissue 78
4.6. Signatures of smectic order in liver tissue 81
4.7. Summary 86
5. Effective models for cell and network polarity coordination 89
5.1. Discretization of a uniaxial nematic free energy 89
5.2. Discretization of a biaxial nematic free energy 91
5.3. Application to cell polarity organization in liver tissue 92
5.3.1. Spatial profile of orientational order in liver tissue 93
5.3.2. Orientational order from neighbor-interactions and boundary conditions 94
5.3.3. Orientational order from coupling to an external field 99
5.4. Biaxial interaction model 101
5.5. Summary 105
6. Network self-organization in a liver-inspired lattice model 107
6.1. Cubic lattice geometry motivated by liver tissue 107
6.2. Effective energy for local network segment interactions 110
6.3. Characterizing network structures in the cubic lattice geometry 113
6.4. Local interaction rules generate macroscopic network structures 115
6.5. Effect of mutual repulsion between unlike segment types on network structure 118
6.6. Summary 121
7. Discussion and Outlook 123
A. Appendix 127
A.1. Mean field theory fo the isotropic-uniaxial nematic transition 127
A.2. Distortions of the Mollweide projection 129
A.3. Shape parameters for basal membrane around hepatocytes 130
A.4. Randomized control for network segment anisotropies 130
A.5. The dihedral symmetry group D2h 131
A.6. Relation between orientational order parameters and elements of the super-tensor 134
A.7. Formal separation of molecular asymmetry and orientation 134
A.8. Order parameters under action of axes permutation 137
A.9. Minimal integrity basis for symmetric traceless tensors 139
A.10. Discretization of distortion free energy on cubic lattice 141
A.11. Metropolis Algorithm for uniaxial cell polarity coordination 142
A.12. States in the zero-noise limit of the nearest-neighbor interaction model 143
A.13. Metropolis Algorithm for network self-organization 144
A.14. Structural quantifications for varying values of mutual network segment repulsion 146
A.15. Structural quantifications for varying values of self-attraction of network segments 148
A.16. Structural quantifications for varying values of cell demand 150
Bibliography 152
Acknowledgements 17
An ensemble learning approach for the classification of remote sensing scenes based on covariance pooling of CNN features
International audienceThis paper aims at presenting a novel ensemble learning approach based on the concept of covariance pooling of CNN features issued from a pretrained model. Starting from a supervised classification algorithm, named multilayer stacked covariance pooling (MSCP), which exploits simultaneously second order statistics and deep learning features, we propose an alternative strategy which employs an ensemble learning approach among the stacked convolutional feature maps. The aggregation of multiple learning algorithm decisions, produced by different stacked subsets, permits to obtain a better predictive classification performance. An application for the classification of large scale remote sensing images is next proposed. The experimental results, conducted on two challenging datasets, namely UC Merced and AID datasets, improve the classification accuracy while maintaining a low computation time. This confirms, besides the interest of exploiting second order statistics, the benefit of adopting an ensemble learning approach
Efficient Clustering on Riemannian Manifolds: A Kernelised Random Projection Approach
Reformulating computer vision problems over Riemannian manifolds has
demonstrated superior performance in various computer vision applications. This
is because visual data often forms a special structure lying on a lower
dimensional space embedded in a higher dimensional space. However, since these
manifolds belong to non-Euclidean topological spaces, exploiting their
structures is computationally expensive, especially when one considers the
clustering analysis of massive amounts of data. To this end, we propose an
efficient framework to address the clustering problem on Riemannian manifolds.
This framework implements random projections for manifold points via kernel
space, which can preserve the geometric structure of the original space, but is
computationally efficient. Here, we introduce three methods that follow our
framework. We then validate our framework on several computer vision
applications by comparing against popular clustering methods on Riemannian
manifolds. Experimental results demonstrate that our framework maintains the
performance of the clustering whilst massively reducing computational
complexity by over two orders of magnitude in some cases
The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning
A diverse number of tasks in computer vision and machine learning
enjoy from representations of data that are compact yet
discriminative, informative and robust to critical measurements.
Two notable representations are offered by Region Covariance
Descriptors (RCovD) and linear subspaces which are naturally
analyzed through the manifold of Symmetric Positive Definite
(SPD) matrices and the Grassmann manifold, respectively, two
widely used types of Riemannian manifolds in computer vision.
As our first objective, we examine image and video-based
recognition applications where the local descriptors have the
aforementioned Riemannian structures, namely the SPD or linear
subspace structure. Initially, we provide a solution to compute
Riemannian version of the conventional Vector of Locally
aggregated Descriptors (VLAD), using geodesic distance of the
underlying manifold as the nearness measure. Next, by having a
closer look at the resulting codes, we formulate a new concept
which we name Local Difference Vectors (LDV). LDVs enable us to
elegantly expand our Riemannian coding techniques to any
arbitrary metric as well as provide intrinsic solutions to
Riemannian sparse coding and its variants when local structured
descriptors are considered.
We then turn our attention to two special types of covariance
descriptors namely infinite-dimensional RCovDs and rank-deficient
covariance matrices for which the underlying Riemannian
structure, i.e. the manifold of SPD matrices is out of reach to
great extent. %Generally speaking, infinite-dimensional RCovDs
offer better discriminatory power over their low-dimensional
counterparts.
To overcome this difficulty, we propose to approximate the
infinite-dimensional RCovDs by making use of two feature
mappings, namely random Fourier features and the Nystrom method.
As for the rank-deficient covariance matrices, unlike most
existing approaches that employ inference tools by predefined
regularizers, we derive positive definite kernels that can be
decomposed into the kernels on the cone of SPD matrices and
kernels on the Grassmann manifolds and show their effectiveness
for image set classification task.
Furthermore, inspired by attractive properties of Riemannian
optimization techniques, we extend the recently introduced Keep
It Simple and Straightforward MEtric learning (KISSME) method to
the scenarios where input data is non-linearly distributed. To
this end, we make use of the infinite dimensional covariance
matrices and propose techniques towards projecting on the
positive cone in a Reproducing Kernel Hilbert Space (RKHS).
We also address the sensitivity issue of the KISSME to the input
dimensionality. The KISSME algorithm is greatly dependent on
Principal Component Analysis (PCA) as a preprocessing step which
can lead to difficulties, especially when the dimensionality is
not meticulously set.
To address this issue, based on the KISSME algorithm, we develop
a Riemannian framework to jointly learn a mapping performing
dimensionality reduction and a metric in the induced space.
Lastly, in line with the recent trend in metric learning, we
devise end-to-end learning of a generic deep network for metric
learning using our derivation
Novel 3D Ultrasound Elastography Techniques for In Vivo Breast Tumor Imaging and Nonlinear Characterization
Breast cancer comprises about 29% of all types of cancer in women worldwide. This type of cancer caused what is equivalent to 14% of all female deaths due to cancer. Nowadays, tissue biopsy is routinely performed, although about 80% of the performed biopsies yield a benign result. Biopsy is considered the most costly part of breast cancer examination and invasive in nature. To reduce unnecessary biopsy procedures and achieve early diagnosis, ultrasound elastography was proposed.;In this research, tissue displacement fields were estimated using ultrasound waves, and used to infer the elastic properties of tissues. Ultrasound radiofrequency data acquired at consecutive increments of tissue compression were used to compute local tissue strains using a cross correlation method. In vitro and in vivo experiments were conducted on different tissue types to demonstrate the ability to construct 2D and 3D elastography that helps distinguish stiff from soft tissues. Based on the constructed strain volumes, a novel nonlinear classification method for human breast tumors is introduced. Multi-compression elastography imaging is elucidated in this study to differentiate malignant from benign tumors, based on their nonlinear mechanical behavior under compression. A pilot study on ten patients was performed in vivo, and classification results were compared with biopsy diagnosis - the gold standard. Various nonlinear parameters based on different models, were evaluated and compared with two commonly used parameters; relative stiffness and relative tumor size. Moreover, different types of strain components were constructed in 3D for strain imaging, including normal axial, first principal, maximum shear and Von Mises strains. Interactive segmentation algorithms were also evaluated and applied on the constructed volumes, to delineate the stiff tissue by showing its isolated 3D shape.;Elastography 3D imaging results were in good agreement with the biopsy outcomes, where the new classification method showed a degree of discrepancy between benign and malignant tumors better than the commonly used parameters. The results show that the nonlinear parameters were found to be statistically significant with p-value \u3c0.05. Moreover, one parameter; power-law exponent, was highly statistically significant having p-value \u3c 0.001. Additionally, volumetric strain images reconstructed using the maximum shear strains provided an enhanced tumor\u27s boundary from the surrounding soft tissues. This edge enhancement improved the overall segmentation performance, and diminished the boundary leakage effect. 3D segmentation provided an additional reliable means to determine the tumor\u27s size by estimating its volume.;In summary, the proposed elastographic techniques can help predetermine the tumor\u27s type, shape and size that are considered key features helping the physician to decide the sort and extent of the treatment. The methods can also be extended to diagnose other types of tumors, such as prostate and cervical tumors. This research is aimed toward the development of a novel \u27virtual biopsy\u27 method that may reduce the number of unnecessary painful biopsies, and diminish the increasingly risk of cancer
Towards cellular hydrodynamics: collective migration in artificial microstructures
The collective migration of cells governs many biological processes, including embryonic development, wound healing and cancer progression. Observed phenomena are not simply the sum of the individual motion of many isolated cells, but rather emerge as a consequence of their interactions. The movements in epithelial cell sheets display rich phenomenology, such as the occurrence of vortices spanning several cell diameters and the transition from fluid-like behavior at low densities to glass-like behavior at high densities. In this thesis, collective invasion of epithelial cell sheets into microchannels was studied on a phenomenological level within the scope of theoretical approaches to active fluids.
In a first project, the motion profile of a cell layer in straight channels was investigated using single cell tracking and particle image velocimetry (PIV) on timelapse microscopy data. A defined plug-flow like velocity profile was observed across the channels. The cell density profile is well-described by the Fisher-Kolmogorov reaction-diffusion equation, which includes active migration and the contribution of proliferation. This study revealed a change in the short scale noise behavior in the presence of this global invasion into a channel.
For a closer look at the system’s proliferation component, the effect of an underlying global migration direction on the orientation of the cells’ division axes was examined. We found strong alignment of the axes’ orientation with the imposed movement direction. Specifically, the strongest correlations were observed between the orientation of the cells’ division axes and the local strain rate tensor’s main axis. This is in agreement with the notion that stresses in the migrating cell sheet orient the cell divisions.
Expanding the assay of invasion into straight channels, we introduced a constriction, which the cell sheet needs to pass through in order to progress. A plateau of low velocities was observed in the region ahead of the constriction, which was attributed to an increase in local cell density accompanied by jamming. These results were compared to an active isotropic-nematic mixture model. The suitability of this model to describe this assay could be ruled out, however, as it showed qualitatively very different behavior than the experiments.
Finally, the frequency of topological nearest-neighbor T1 transitions within a cell sheet was investigated in minimal model systems. In order to study the smallest possible fundamental unit for such transitions, groups of four cells were confined to cloverleaf patterns, which could be shown to inhibit the onset of collective rotation states. Results showed that T1 transitions occurred more frequently for groups of cells with a lower average length of the cell-cell junction that shrinks in the process of this transition. These results are consistent with the notion that the energy barrier which needs to be overcome by the cells in order to perform this transition, scales with the original length of the shrinking junction.
Taken together, the results of this thesis contribute to a better understanding of the flow fields for collective cell migration processes in confined geometries. In addition to the insights the phenomenological observations in this work could provide directly, they will also continue to prove useful as a standard for validating detailed theoretical models
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